The solutions of the model with an
interaction term (REF )
(\(i.e.\) 
with a linear coupling function \(f(\phi )=\phi \) )
have been extensively studied in the literatureFor a review of the literature
together with an investigation of spinning solutions, see the recent work [1]}.,
starting with
Refs. [2]}, [3]},
falling within
the Horndeski class of scalar-tensor theories of gravity [4]}.
The results in this work show that
the term \(\phi L_{GB}\) 
naturally occurs also in this topological construction leading to HCSG models.
This model is rather special,
the equations of motion
being invariant
under the transformation
\(\phi \rightarrow \phi +\beta \) 
(with \(\beta \)  arbitrary),
which leads to a conserved current.
The coupling function \(f(\phi )=\phi \) , however, does not allow for
BH scalarization:
the condition
(REF ) is not fulfilled.
